In a typical telephone or communications channel of the public switched telephone network (PSTN), for example, portions of the channel may generate undesirable signal reflections or echoes. In particular, the transition between a two-wire circuit and four-wire circuit at a hybrid may generate an undesirable echo if impedances between the two circuits are not properly matched at the hybrid. For a voice signal being reflected back upon the speaker, a somewhat hollow or singing tone may be heard. If the echo has a sufficient delay, delayed intelligible speech may be heard by the speaker. The effect of an echo on a data signal may be to delay or spread the energy, perhaps causing intersymbol interference.
Hybrid repair or replacement, or the addition of an echo canceler may be readily effected once the source of the echo is determined. Accordingly, echo characterization or monitoring may be routinely performed by the telephone service provider. In particular, non intrusive, in-service testing of circuits for speech echo path loss (SEPL) and speech echo path delay (SEPD) may be performed. (See, ANSI Std. T1.221-1991 entitled "In-service Non Intrusive Measurement Device (INMD)"--Voice Service Measurements).
Because of the relatively large number of lines extending from a central office of the PSTN, it may be desirable to quickly and accurately test a significant number of the lines. Moreover, because a communications channel typically includes several portions or individual lines connected only for a particular call, in-service non intrusive testing is highly desirable. Not only does such testing detect echo problems permitting their correction, it also permits documentation of high quality service to users.
U.S. Pat. No. 4,947,425 discloses a digital signal processor to range and converge on each of a plurality of echoes occurring at respective echoes along a communications channel. The device adaptively filters or processes samples of a signal that has been transmitted along the communications channel correlated with samples of a signal received from the channel. The digital signal processor emulates three cascaded adaptive finite impulse response (FIR) filters. The output response of each filter obtained from a current sequence of samples of the transmitted signal convolved with the coefficients of the respective filter is processed with a corresponding sample of the received signal to provide an error signal. A time domain least-mean-squares (LMS) approach or algorithm, in turn, is used to process the error signal to generate a new set of filter coefficients which, in turn, are used to filter the next sample of the transmitted signal.
The LMS operation is repeated until the error signal reaches a minimum, thereby indicating convergence upon the echo. When a respective FIR filter converges on an echo, the digital signal processor uses the last set of filter coefficients to generate a measurement of echo path loss.
The transversal adaptive filter using the least mean square (LMS) algorithm of Widrow and Hopf has been widely used mainly due to its relative ease of implementation. (See B. Widrow et al., "Stationary and nonstationary learning characteristics of the LMS adaptive filter," Proc. IEEE, vol. 64, pp. 1151-1162, Aug. 1976). The major drawback of this time-domain LMS (TDLMS) algorithm is that as the eigenvalue spread of an input autocorrelation matrix R increases, the convergence speed of the algorithm decreases as discussed in J. C. Lee and C. K. Un, "Performance of transform-domain LMS adaptive signal filters," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 499-510, June 1986. This shortcoming led to the consideration of transform domain adaptive filters where the input signals are orthogonalized.
The transforms can be generally thought of as a set of parallel tuned filters. The filtering view of transforms is also able to predict the performance of the transform domain adaptive filter and suggests the transforms that suit specific applications. (See, for example, B. Farhang-Boroujeny and S. Gazor, "Selection of orthonormal transformers for improving the performance of transform domain normalised LMS algorithm," IEEE Proceedings, Part F: Radar and Signal Processing, vol. 139, pp. 327-335, Oct. 1992). The new transformed set of samples, with minimum correlation among them, is then normalized in proportion to the inverse of the energy of the individual taps, thus accelerating convergence. Another advantage of transform domain algorithms is increased computational efficiency due to block processing. The efficiency of an orthonormal transform, in improving the performance of the LMS algorithm, depends on its ability to spread the energy levels of its output components, i.e., the ability to reduce the crosscorrelation between the transformed samples.
Research has also shown that transformation without normalization does not improve performance of the adaptive filters as discussed in B. Farhang-Boroujeny and S. Gazor, "Selection of orthonormal transforms for improving the performance of transform domain normalised LMS algorithm," IEEE Proceedings, Part F: Radar and Signal Processing, vol. 139, pp. 327-335, Oct. 1992. This is because the autocorrelation matrix R and the transformed matrix R.sub.T are similar matrices with the same eigenvalues. Transformation is useful in attempting to diagonalize R; however, the normalization process tends to make the eigenvalues, that is, the rate of convergence of the different modes, equal. Also, orthonormal transformation followed by normalization typically does not degrade the performance of the LMS algorithm. (See, B. Farhang-Boroujeny and S. Gazor, "Selection of orthonormal transforms for improving the performance of transform domain normalised LMS algorithm," IEEE Proceedings, Part F: Radar and Signal Processing, vol. 139, pp. 327-335, Oct. 1992).
Unfortunately, the major drawback of time-domain LMS (TDLMS) approaches for echo characterization is that such approaches are relatively slow. In addition, computational complexity must also be considered in implementing an approach to reduce cost. The effects of return noise present on the communications channel may also require consideration for accurate measurements.